Defining parameters
| Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1568.cf (of order \(84\) and degree \(24\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 784 \) |
| Character field: | \(\Q(\zeta_{84})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(448\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1568, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5472 | 0 | 5472 |
| Cusp forms | 5280 | 0 | 5280 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)